There has been an abruptly growing demand on information transmission in association with a recent widespread use of personal computers and the Internet, so optical transmission with a high transmission rate has become widespread. An optical waveguide has been used as an optical interconnection in such optical transmission.
When a 1×2 branching section is constituted, for example, in the case where a branching and coupling device for optical transmission is constituted, in junctions where two curved optical waveguides connect with a branching section (outlets of a branching section of the optical waveguide), gradually widening a gap between both the curved optical waveguides from an infinitesimal one is an ideal way effective in reducing an excessive loss at a branching section. However, it is extremely difficult to form an infinitesimal gap in high yield and to widen the gap from an infinitesimal one gradually owing to restrictions upon production. Accordingly, at the junctions of the curved optical waveguides with the outlets of the branching section of the optical waveguide, the occurrence of axial deviation can suppress the excessive loss at the branching section. That is, each mode center causes axial deviation toward an inner side, so both the curved optical waveguides can be connected with the branching section with a low loss even when the gap between both the curved optical waveguides is widened. As described above, widening the gap between both the curved optical waveguides can not only reduce an influence of a variation upon production in shape of the branching section but also alleviate embedding failure at a narrow width part that may occur by a clad material. To this end, a circular-arc type curved optical waveguide can be effectively used.
A radius of curvature at each of both ends of a curved optical waveguide using a circular arc is finite. Accordingly, a curvature changes discontinuously at the junctions when the curved optical waveguide connects with a straight line-optical waveguide. As a result, the central axis of a propagation mode causes axial deviation with respect to the geometrical central position of a waveguide structure. Accordingly, the waveguide structure at the junction must be provided with axial deviation for improving mode matching at the junction to provide a waveguide causing a low loss. Since an axial deviation amount depends on a relative refractive index between a core and a clad, the dimensions of the core, and a wavelength, the fact that fluctuations in the refractive index and the dimensions of the core due to variations upon production are responsible for a fluctuation in loss has been a problem. The incapability to provide an optimum axial deviation amount in a wide wavelength range due to wavelength dependence has been also a problem.
On the other hand, when a circular-arc type curved optical waveguide is used in an inlet of a branching section of the optical waveguide, a mode center causes axial deviation and a mode shape asymmetric with respect to a central axis is established owing to a finite radius of curvature. Accordingly, it has been difficult to establish a symmetric branching ratio (1:1). In addition, an axial deviation amount and asymmetry are different at different wavelengths, so it has been difficult to keep a branching ratio constant in a wide wavelength range. In view of the foregoing, an approach to connecting a straight line-optical waveguide with an inlet of a branching section of the optical waveguide is adopted. However, the approach involves a disadvantage in that an excessive loss occurs at a junction of the straight line-optical waveguide with a curved optical waveguide and a disadvantage in that the total length of an optical waveguide increases so that the size of the optical waveguide increases.
That is, the connection of a circular-arc type curved optical waveguide with an outlet of a branching section of the optical waveguide is advantageous. On the other hand, an optical waveguide having an infinite radius of curvature (a curvature of zero) such as a straight line-optical waveguide is preferably connected with an inlet of a branching section of the optical waveguide for establishing a symmetric branching ratio (1:1).
When the shape of the optical waveguide (core) is of a curved type such as an S-shape curve, the central axis of an optical propagation mode deviates from the geometrical central axis of the core at a part where a curvature thereof changes discontinuously. As a result, an optical loss occurs. To reduce the loss, part of a curve must be provided with an axial deviation structure part (offset) in which the geometrical central axis of the core is deviated. However, such axial deviation structure depends on a relative refractive index between the core and a clad, the dimensions of the core, and a light wavelength. Accordingly, it is difficult to provide an optimum axial deviation structure owing to factors such as a variation upon production. In general, the absence of an axial deviation structure is preferable because otherwise a problem arises in that an optical loss occurs. The incapability to provide an optimum axial deviation amount in a wide wavelength range due to wavelength dependence has been also a problem.
Here, several functions of creating a curved shape in an optical waveguide or the like in CAD software or the like have been known. One shape is a shape in which two arcs each having a radius of curvature of R are connected in an opposite direction (hereinafter referred to as the arc coupling shape). Since a curvature changes discontinuously at a junction in the arc coupling shape, the junction where the arcs are connected must be provided with an axial deviation structure as described above.
A shape using the following cosine function (referred to as S-bend cosine on CAD software) has been also known. The shape eliminates the need for providing the above-described axial deviation structure on a halfway.y=1/2(1−cos πz)  [VIII]
However, a curvature at each of both ends of the shape is finite, so the joining of the shape with a straight line-optical waveguide involves the need for providing an axial deviation structure (FIG. 2).
In addition, a shape using the following sine function (referred to as S-bend sine on CAD software) eliminates the need for providing a curve with an axial deviation structure on a halfway. In addition, a radius of curvature at each of both ends of the shape is infinite (a curvature is zero). Accordingly, when the curved optical waveguide is joined with straight line-optical waveguides at its both ends, the central axes of the curved optical waveguide and of the straight line-optical waveguides coincide with each other, so there is no need for providing an axial deviation structure.y=z−(1/2π)sin 2πz  [IX]
Some documents (see, for example, Non-patent Document 1 below) each have general description concerning such axial deviation structure of an optical waveguide.
There has been also proposed a branching/multiplexing optical waveguide in which a junction between the inflection point of a branching section of the optical waveguide and an output waveguide is provided with axial deviation, and a gap is provided between the branching waveguides at the branching point of a taper waveguide so that the deviation of peaks of a field distribution in a curved optical waveguide can be covered (see Patent Document 1 below).
There have been also proposed an optical coupler using an optical waveguide having many arcs to facilitate modularization and a method of manufacturing thereof (see Patent Document 2 below).    Non-patent Document 1: Light Wave Engineering, Yasuo Kokubu, KYORITSU SHUPPAN CO., LTD, p 250    Patent Document 1: JP 2809517 B    Patent Document 2: JP 2002-530690 A